@keith All other tires of sidewall is OK as well. I have no idea when valve core is loose. I just found the leaking area is around the valve after I stopped and found the tire is flat. It may started to leak days or weeks ago. I only had another shop did the oil change 5 months ago. I added air by myself every one or two months with a inflator bought from Amazon. It uses screw-on nozzle to connect to valve during the inflation. I am not sure if this could be a potential risk. Should I use valve core tool to tighten it every time when I inflate the tire in the future? No one pranked me. The rim in the picture is the brand new rim installed on Wednesday. No loose lug is found that day. The picture shows the new rim with old tire which the shop said is OK. I drive it for two days and I do not feel any problem. But all trips are short and slow and no highway driving.
I hope so. But I learned a lot from internet strangers 
There is nothing to be learned here, this in nothing more than a folly.
The price of tires has gone up, the least costly tire for your car listed on Tire Rack is $101, Bridgestone. How much were the Goodride tires?
There is a sale on these tires, buy one and get three free.
Goodride tire I bought is CAD$123 (USD$90) each. Buy one get 3 free is really good deal. No problem to buy new tire. I donāt know much about car related stuff and only started to drive 7 years ago. So I did learn a lot here. Thanks for the tire information.
That was humor, not a real offer. I donāt endorse tires from unknown Chinese
companies. Windforce?
An inexpensive tire like Goodride might be adequate for your city driving. I wouldnāt put expensive tires on a taxi.
I have never seen a screw on nozzle loosen up a valve core. I have never used a valve core tool to tighten valve cores after adding air although when I have a tire that is loosing air very slowly, I do check that the valve core is seated with a valve core tool. I have never found on loose in a tire but I did find a loose valve core in an AC system one time. Not sure how it got loose but I had just checked the system pressure with a two gauge set.
Not exactly sure what you mean, but I had a leak from the valve stem w/ valve core on one of my truckās tires one time, fixed by just re-tightening the core so it seated properly, using a valve core tool. I use that tool mostly for bicycle repairs, but came in handy for the car that time.
This is an example of a screw on nozzle.
Instead of clamping on the valve stem, it screws on. These were the standard through the 60ās until the clamp on type came out. I think the OP was thinking that while unscrewing the nozzle from the valve stem, it could somehow catch the core and unscrew it also. All the ones I have ever used, including the one in the link above, only the outside of the body turns. The inside is prevented from turning by a solid connection to the hose.
OK, thanks for clarification I see what you mean, and concur, screw-on nozzle unlikely to blame for loose valve-core. I never screwed anything onto my truckās valve stem yet the core had loosened.
@keith @George_San_Jose1 thanks for comments. I agree. Now what I can do now is keeping checking tire pressure frequently and trying to find the slow leaking at the early stage. Then spray soap water or ask repair shop to help.
Ask your shop to check for rim leaks as well.
From the picture you submitted, every experience I have had with flat or nearly flat tires indicates that that tire was never run flat or even low enough to do damage. I donāt know why your valve core would suddenly come loose like it did but I suspect that it started loosing significant air right as you started driving, you felt it and stopped before it go low enough to do any damage, but by the time you got out of the vehicle, it was now flat. So it was pretty much a sudden loss and not a gradual one.
I know that you are pretty sure you werenāt pranked, but to me, that is the most logical explanation, but there could be others.
Yes. Probably that is the case or it is very short distance and slow speed when it is completely flat.
I would think that the problem has been resolved in the last 3 months.
If not, then the OP can start a new thread titled āI drove on a completely flat tire for three hundred miles. Should I replace it?ā.
While the problem was solved, others with similar issues might value another opinion. Welcome to the forum @veretilnyk_183862. You are welcome to post on old threads or new ones.
It depends on whether the purpose of a forum is a tight knit community that only involves themselves, or if the purpose is to produce content that strangers coming in from search engines can see.
There really needs to be a option on the forum to respond to an old topic but not have it bump to the top. Rather than complain here, why not go submit a feature request to the developers?
I say move the questionable tire to the front right. If it blows it wonāt cause a spin out, and it will tend to steer off the road to the right, instead of in to oncoming traffic.
That has little affect. The āask someā section is still very annoying.
I would not replace it but I might put it in the back. Passenger side so I could keep a better notice of it.
I would leave it on the frontthe drop and swerve of a blowout is more severe on a rear tire and if it is on the front it is easier to correct because you can steer the front. I have found loose valve cores, I just assumed they were no properly tightened when manufactured.
For the OP ue , I would not spend 5 minutes worrying about that tire. I canāt see how all the contradictory advice can help him though.